Off-shell Gauge Fields from BRST Quantization

TL;DR

This paper introduces a novel approach to constructing nonlinear off-shell gauge field theories using deformation quantization and BRST formalism, leading to new insights into higher-spin theories on AdS backgrounds.

Contribution

It develops a new method combining BRST quantization with unfolded formalism and AKSZ procedures to formulate off-shell gauge theories, exemplified by higher-spin fields.

Findings

Derived off-shell higher-spin gauge theory on AdS background.

Connected BRST quantization with unfolded formalism for gauge theories.

Demonstrated the approach with a quantized scalar particle example.

Abstract

We propose a construction for nonlinear off-shell gauge field theories based on a constrained system quantized in the sense of deformation quantization. The key idea is to consider the star-product BFV--BRST master equation as an equation of motion. The construction is formulated in terms of the BRST extention of the unfolded formalism that can also be understood as an appropriate generalization of the AKSZ procedure. As an application, we consider a very simple constrained system, a quantized scalar particle, and show that it gives rise to an off-shell higher-spin gauge theory that automatically appears in the parent form and properly takes the familiar trace constraint into account. In particular, we derive a geometrically transparent form of the off-shell higher-spin theory on the AdS background.